1. Relativistic Chiral Mean Field Model for Finite Nuclei
Hiroshi Toki (RCNP/Osaka)
in collaboration with
Yoko Ogawa (RCNP/Osaka)
Setsuo Tamenaga (RCNP/Osaka)
Akihiro Haga (Nagoya/RCNP)
2018/11/24
May 19 Shanhai 2006

2. 6500 light year away 1987A is 150,000 light year away From Sumiyoshi
From Book by N. Itoh
From Gravitation by Misner, Thorn, Wheeler
6500 light year away
1987A is 150,000 light year away
2018/11/24
May 19 Shanhai 2006
From Sumiyoshi

3. 超新星爆発 February 23, 1987 Before After
Supernova is not yet exploded by theory!!
Neutrino He4 GT reaction is key
2018/11/24
May 19 Shanhai 2006

4. Ab initio calculation of light nuclei
Pion
70 ~ 80 %
C. Pieper and R. B. Wiringa, Annu. Rev. Nucl. Part. Sci.51(2001), nucl-th/
2018/11/24
May 19 Shanhai 2006

5. Resolution Now and Then
Y. Fujita et al.,
EPJ A 13 (’02) 411.
H. Fujita et al.,
Dr. Th. & PRC
2018/11/24
May 19 Shanhai 2006

6. Experiments H. Fujita et al (RCNP) 2003 Tamii for (p, p’)
High resolution GT (pionic) excitations
High resolution (30keV)
H. Fujita et al (RCNP) 2003
Tamii for (p, p’)
2018/11/24
May 19 Shanhai 2006

7. Weinberg transformation
Chiral sigma model
Y. Ogawa et al. PTP (2004)
Pion is the Goldstone boson of chiral symmetry
Linear Sigma Model Lagrangian
Polar coordinate
Weinberg transformation
2018/11/24
May 19 Shanhai 2006

8. Non-linear sigma model
Lagrangian
r = fp + j
where
M = gsfp M* = M + gs j
mp2 = m2 + l fp2
ms2 = m2 +3 l fp2
mw = gwfp mw* = mw + gwj ~
2018/11/24
May 19 Shanhai 2006

9. Mean Field Equation Surface pion condensation Dirac equation
Klein-Gordon equations
Surface pion field
2018/11/24
May 19 Shanhai 2006

10. Nuclear matter Chiral sigma model vs. TM1 Density = 0.1414 fm-3
E/A = MeV
K = 650 MeV
ms = 777 MeV
mw = 783 MeV
mp = 139 MeV
M = 939 MeV
fp = 93 MeV
l = (ms2 - mp2) / 2fp2 =
gs = M / fp =
gw = mw / fp = = h gw
h = ~
2018/11/24
May 19 Shanhai 2006

11. 40Ca 56Ni gp = gA/2fp h = 1.17319 with pion (gA = 1.15) without pion
9.2
40Ca
N=20
56Ni
9.0
N=28
8.8
8.6
8.4
8.2
8.0
7.8 20 30 40 50 60 70 80 90
N=Z
A (Mass number)
with pion (gA = 1.15)
without pion
gp = gA/2fp
2018/11/24
May 19 Shanhai 2006
h =

12. 56Ni Magic effect No pion Pion Mean Field Parity mixed
Pion produces spin-orbit splitting!!
2018/11/24
May 19 Shanhai 2006

13. Gamow-Teller transition
2018/11/24
May 19 Shanhai 2006

14. Relativistic Mean Field Theory with Pion
(0-) s, w
Parity mixed
self-consistent
mean field +
Single particle state with parity mixing
Intrinsic state (parity mixed state !!)
H. Toki, S. Sugimoto, and K. Ikeda, Prog. Theor. Phys. 108(2002)903
2018/11/24
May 19 Shanhai 2006

15. Symmetry projected RMF with pion
2018/11/24
May 19 Shanhai 2006

16. Charge and parity projected RMF
2018/11/24
May 19 Shanhai 2006

17. projection -2-
2018/11/24
May 19 Shanhai 2006

18. Energy components and radius
Y. Ogawa et al., PRC73 (2006) 34301
2018/11/24
May 19 Shanhai 2006

19. Parity projection
Wave function
2018/11/24
May 19 Shanhai 2006

20. Density distribution and form factor
2018/11/24
May 19 Shanhai 2006

21. He4 and He5
Myo et al (2005)
2018/11/24
May 19 Shanhai 2006

22. Phase shifts for various partial waves
2018/11/24
May 19 Shanhai 2006

23. Higher partial waves
2018/11/24
May 19 Shanhai 2006

24. Conclusion
We have developed the relativistic chiral mean field model for finite nuclei
Spin and charge projection is essential
Chiral symmetry recovery of 20% provides strong attraction for nuclear formation
Pion provides a half of spin-orbit splitting
We have succeeded to have renormalized chiral meson-baryon Lagrangian (vacuum)
2018/11/24
May 19 Shanhai 2006

25. Coleman-Weinberg mechanism for Renormalization of Chiral Sigma Model
Linear sigma model
Work out the nucleon loop and boson loop
2018/11/24
May 19 Shanhai 2006

26. Total effective potential
Final Lagrangian
2018/11/24
May 19 Shanhai 2006

27. Results Quantum corrections cancel each other and the
theory becomes trivial.
2018/11/24
May 19 Shanhai 2006

28. Coleman-Weinberg Scheme for Chiral Symmetric Lagrangian
Massless Fermion-Chiral Boson system
There is Fermion-Boson symmetry at
m=infinity  No loop corrections
Slight symmetry braking provides divergence free reasonable size non-linear effective potential
We get now the lagrangian for finite nuclei with the vacuum contribution worked out
2018/11/24
May 19 Shanhai 2006